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3) f = 2π ρ L2 49 50 3 Cantilever Conversion Tables Next, define two material-related constants, c1 and c2 , by c1 = 1 2π 3E ρ c2 = 3π E. 5) Selecting a given cantilever material dictates the values of c1 and c2 . 9) and respectively, by the two equations and which involve the parameter set { L, r, k, f }. The solution of these two equations gives the value of each parameter in terms of two others. 1, where each parameter is expressed in terms of two other parameters. 2 for a cantilever made of PtIr.

It is therefore of interest to examine the ratio of the angular and linear spring constants, given by the function ξ z ( x ), ξ z (x) = k θz ( x ) . 17) Inserting Eq. 11) and Eq. 16) into Eq. 17) gives ξ z (x) = 3(2L − x ) x . 2 Bending Due to Fz The function ξ z ( x ) is used by the software of the AFM to calibrate the tip– sample force using the specifications of the particular cantilever in use. 6 Numerical Example: Si We can now present numerical examples for the response of the Si cantilever to a force acting in the zˆ direction.